The Mixed Disc Packing Problem: Part I: Some Bounds on Density

Abstract

Packing problems in general constitute a difficult set of problems which still defy solution The determination of bounds on the solution of such problems can, however, provide insight concerning the problem and can help in the development of new solution procedures. This paper, Part I, develops some bounds on the density of packing mixed discs on a circular plate. A methodology is proposed which formulates the problem as a linear program and requires the generation of feasible packings. The procedure for testing feasible packings, the solution algorithm, and results of experimentation are discussed in Part II, to appear in the next issue.